About eigensteve Expertise Any questions about introductory or advanced calculus, real or complex analysis, linear algebra, or ordinary differential equations are fair game. I can answer questions about specific calculations, derivations, proofs, and physical applications. Your questions are as good for me as they are for you!
Experience I use linear algebra and differential equations almost every day for my research on modeling unsteady aerodynamics. In particular, my research experience includes numerical integration of trajectories, stability analysis of fluid flow fields, numerical computation of Lyapunov exponents, and more.
Organizations SIAM
AIP
APS
AIAA
IEEE
Publications AIAA Aerospace Sciences Meeting and Exhibit [2008, 2009].
IEEE Photovoltaic Specialist [2009].
For these publications, see http://carlsbad.princeton.edu/~steve/papers/
Education/Credentials I earned my B.S. in Mathematics from Caltech in 2006. I am currently a PhD. Candidate in Mechanical and Aerospace Engineering at Princeton. I expect to graduate in 2011.
Awards and Honors Athena-Feron Scholarship Award for Excellence in Mathematical Coursework [2007],
Princeton MAE Second Year Fellowship for Research Excellence [2007],
Gordon Wu Fellowship [2006-2010],
Caltech Summer Undergraduate Research Fellowship [2003-2005].
Calculus - TRIGONOMETRY (trigonometric functions) but not sure if this is also included with it
Expert: eigensteve - 6/20/2009
Question Hi myy name's Veronica and I'm currently having trouble
answering these problems. I believe they have to be verified
using the pythagorean identities (i think) but my notes are
only about the sin, cos, tan, etc. I dont have notes about
these kind of problems. Please help me. Thanks.
Problems:
1) Verify: sin(theta)cos(theta)=x(square root of 25-x^2) all
over 25. where theta is an acute angle of triangle ABC withe
one side x.
2) tan^2A=x^2 all over 9-x^2
3) 4sin^2A over cosA= x^2 all over square root of 16-x^2
I will Be waiting for your answers.. Please help me I would
greatly appreciate it.. Thanks again.
Answer Hi Veronica,
I believe that the way to approach this problem is by using a sketch of a triangle and what we know about sin, cos, tan.
Imagine I have a right triangle with sides x, y and hypotenuse z. From the Pythagorean theorem, we know that z^2 = x^2 + y^2.
Lets assume that theta is the angle between the side of length x and length z. We know that
Finally, because the problem has the numbers 25, 9, and 16 in it, I know that they are talking about a /specific/ right triangle with sides 3,4,5. This makes sense, since the Pythagorean theorem states that:
3^2 + 4^2 = 5^2
which is just
9 + 16 = 25
So now that you know that you are dealing with a right triangle with sides 3,4,5 you should be able to use the info above to solve this.
